Title:  Numerical Simulation for Bose-Einstein condensation

Abstract:

   In this talk, we present numerical methods to compute
ground states and dynamics of Bose-Einstein condensates (BEC).
As preparatory steps, we take the 3d Gross-Pitaevskii equation (GPE),
scale it to obtain a three-parameter model and use an approach
well known in the physical literature to reduce it to 2d and
1d GPEs in certain limiting regimes. Two numerical methods are
presented to compute the ground and excited states and a
time-splitting spectral method is used to solve the
time-dependent GPE for dynamics. Then the numerical methods are
applied to study collapse and explosion of BEC, as well as
stability and interaction of central vortex states in BEC.
Comparison of our numerical results and experiment data
are also presented.